Question

The Carnot efficiency of a heat engine depends on the temperature of the:

• A. Hot reservoir only
• B. Cold reservoir only
• C. Difference between the hot and cold reservoirs
• D. Volume of the engine

Hint:

For a heat engine to be most efficient, the difference in temperature between the hot and cold reservoirs should be maximized.

Answer 1

The Correct Option is C

The Carnot efficiency of a heat engine is a theoretical measure of the maximum efficiency that any heat engine can achieve when operating between two reservoirs. The formula for the Carnot efficiency is: \[ \eta = 1 - \frac{T_c}{T_h} \] where:
\( \eta \) is the efficiency,
\( T_c \) is the temperature of the cold reservoir,
\( T_h \) is the temperature of the hot reservoir.
Step 1: The efficiency depends on the temperatures of both the hot and cold reservoirs. However, it's important to note that the Carnot efficiency is determined by the difference between the temperatures of these two reservoirs, not just the temperature of one reservoir.
Step 2: The greater the difference between the hot and cold reservoirs, the higher the efficiency. If the temperature of the cold reservoir is very low and the temperature of the hot reservoir is very high, the efficiency will be closer to 100%. However, in practice, this ideal efficiency cannot be achieved due to practical limitations. Thus, the correct answer is Difference between the hot and cold reservoirs.
Step 3: The volume of the engine is not a factor in the Carnot efficiency, as the efficiency is a function of temperature, not volume or size of the engine.